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Ian Stewart and David Tall

The Foundations of Mathematics

University level mathematics can be a daunting subject, and if you haven't studied maths to this level then you may think that those who have are speaking a different language. Well help is at hand in the form of a short book, The Foundations of Mathematics, by Ian Stewart and David Tall.

The book starts with a gentle introduction to ways of thinking about numbers and number systems. It then gets on to set theory, mathematical logic and formal proofs. The third part looks at number systems defined axiomatically, including the natural numbers, the real numbers and the complex numbers. The final chapter describes where axioms can lead, looking at axiomatic (as opposed to naive) set theory. Gödel's Incompleteness theorem is mentioned briefly - I couldn't help thinking that a whole chapter on this would have made a good finale.

The book would be useful to several different types of reader. Firstly, it would help those who are intending to study mathematics at university to prepare for what might be a difficult start. Secondly, it will be of use to those studying other sciences who want to understand their more mathematical colleagues. More generally, it will appeal to anyone who wants to get a grasp of the foundations of mathematics. The book has exercises for the reader in each chapter, and is well suited to independent study. Overall, I felt that the authors manage to deal with the foundations of mathematics in a way that doesn't get intimidating for the reader.

Amazon.com info
Paperback 280 pages  
ISBN: 0198531656
Salesrank: 706070
Weight:0.97 lbs
Published: 1977 Oxford University Press
Amazon price $29.76
Marketplace:New from $29.76:Used from $1.99
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Amazon.co.uk info
Paperback 280 pages  
ISBN: 0198531656
Salesrank: 31214
Weight:0.97 lbs
Published: 1977 Oxford University Press, USA
Amazon price £41.99
Marketplace:New from £10.00:Used from £0.01
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Amazon.ca info
Paperback 276 pages  
ISBN: 0198531656
Salesrank: 619869
Weight:0.97 lbs
Published: 1995 Oxford University Press
Marketplace:New from CDN$ 77.84:Used from CDN$ 1.24
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Product Description
"There are many textbooks available for a so-called transition course from calculus to abstract mathematics. I have taught this course several times and always find it problematic. The Foundations of Mathematics (Stewart and Tall) is a horse of a different color. The writing is excellent and there is actually some useful mathematics. I definitely like this book."--The Bulletin of Mathematics Books